Tahini or tashi as it is called in Cyprus, is a paste made from ground sesame seeds. It is usually very thick and if left a long time you will see that oil is gathered on top. You do not have to worry about that you just mix it and it is just fine.
To make the tahini sauce or dip this paste has to be dissolved with water, mixed with several other ingredients until it resembles like a creamy mayonnaise.
The recipe is included in my cookbook Mint, Cinnamon & Blossom Water, Flavours of Cyprus, Kopiaste!