What is the purpose of Y-shaped adapters in Illumina sequencing?
Normally, when you need two unique adapters, say A &amp; B, on either end of unknown insert sequences, cohesive-end ligation is difficult because the insert sequences are "unknown". So you have to do blunt-end adapter ligation, in a reaction containing Unknown Inserts + adapter A + adapter B. This can result in 3 possible versions of insert-ligated product: A-insert-A, B-insert-B and A-insert-B, among which only A-insert-B is the only desired product. 

1) Ligation of A-tailed inserts with Y-adapters gives you 100% A-insert-B. 

2) Lets now assign a directionality to the insert - say from base 1 to base 400. Following Y-adapter ligation, you will have 2 kinds of insert-ligated products per insert: A-Insert (1-->400)-B and A-Insert(400-->1)-B, both of which are very useful. Each will create a separate clonal cluster and you will get sequence information starting at both base 1 and base 400 of the insert, since in single-read sequencing, the instrument always sequences from Adapter A. However, to know that both these sequences belong to the same insert, one will need to do paired-end sequencing.