I highly recommend the book Heart of Wisdom from Tharpa Publications as it goes into very practical depth about the two truths and their relationship to one another.
This subject is the most elaborate and challenging subject of Buddhist philosophy, and the most important. To really understand it, it is necessary to study, contemplate, and meditate on authentic instructions about it for a long time because there are many sublte points, and such understanding cannot come from intellectual pursuit alone.
Briefly though, from 8 Steps to Happiness: "Whatever exists is either a conventional truth or an ultimate truth, and, since utlimate truth refers just to emptiness of inherent existence, everything except emptiness is a conventional truth. The things we see directly, such as houses, cars, and tables, are all conventional truths." An example of ultimate truth emptiness is the lack of inherent self-existence of such objects.
Conventional truths have gross and subtle levels of dependent-relationship. However, to understand this clearly, we have to distinguish precisely between conventional objects that do exist, and the objects that do not exist but are conceived to exist by the mind of self-grasping ignorance. By distinuishing these, we can come to a correct understanding of ultimate truth emptiness.
It may seem complicated, but with familiarity and correct explanation, it becomes easier to understand and experience.
Conventional objects appear to be inherently existent. This means they appear to exist from their own side as self-existent, self-propelled, self-made, self-standing and independent of all other phenomena. Of course, immediately we can intellectually say 'of course things depend on other things', but what we're looking at precisely is how the mind perceives and conceives phenomena to exist prior to intellectually dismissing the point.
Conventional objects are totally interdependent upon causes and conditions, parts, name, their basis of imputation (conceptual designation, naming, assigning characteristics and functions), and imputation by consciousness. Because conventional objects are dependent-related, because they have parts, this is the opposite of being independent. We see an independent object where there is no such thing. 'Independent', 'single' or 'one thing' are all names conventionally designated to single objects, but the ultimate reality, the ultimate truth of the object is that there is no real single object there. It is empty of inherent existence, and it is because it is empty of independent existence that it can arise in depedence upon a variety of factors. Indeed, objects of cognition can only appear to our senses and mental consciousness because they are not independent. If they were independent of our mind, how could we perceive them; and if they were independent of other factors, how could they arise? A table is made up of many things that are not table. How can something exist without being made up of other factors? It cannot. Even 'God' is a name imputed by consciousness. God is empty of inherent existence and therefore dependent-related. Thus, it follows that the ultimate truth of all phenomena is emptiness, and mind is the creator of all objects of cognition.
In short, we do a conventional search by looking for an object, and when we find it we say this is the object. But if we look more closely in an ultimate search, trying to find the real object, we find the absence of the thing we're looking for. Why? Because it doesn't really exist in the way it appears to.
Emptiness is not nothingness. Things do exist, but they exist differently from how they appear and are conceived to exist by ordinary beings. By realizing emptiness directly in deep meditation, we attain permanent liberation from suffering.
Why is this? The universal law of cause and effect applies to the person. It is called 'karma'. There is an intimate connection between mind and the phenomena that appear to it. Intentions create mental, verbal, and physical actions, and these leave an impression or seed in the mind - causes. When conditions come together, the seed (cause)ripens as an appearance to mind (effect).
Suffering has causes. The main cause of suffering is self-grasping ignorance because due to this mind, we cherish a self that doesn't really exist, develop attachment for pleasing objects and hatred for displeasing objects and thru the generation of many layers of delusion and contaminated actions, we produce experiences that are contaminated and in the nature of suffering. If we cut ignorance, the root, then the trunk of self-cherishing, the branches of root delusions, the twigs of secondary delusions, and the fruits of suffering will all disappear and cease to function to produce causes and effects.
There is so much that can be said. That is why I recommend the book, as well as meeting teachers who have experience of the subject and can help clarify doubts and misunderstandings. It is very easy to misunderstand the subject because it almost sounds like we're saying things don't exist. When the practitioner clearly understands what the conceived object of self-grasping is in their own experience, then the rest of the analysis is very easy and leads to wonderful results. That is a fact! So please be patient and vigilant and the liberating paths will blossom in your mind.
warm regards,
goodness