Because of wifi connection issue, I have disabled completely IPV6 on my phone.
What bad could possibly happen ? Could some functionality/app be broken ?
If there is any way to solve your problem other than disabling IPv6 on your device, you should do that instead. For instance, if the problem is an old home router that doesn't support IPv6 properly, update its firmware (if that fixes the problem) or replace it.
It might not have much of a noticeable impact on you today, but these are the things you should expect:
Accessing web sites which have already deployed IPv6 (and are using both IPv4 and IPv6, which is known as "dual stack") will usually be slower, because IPv4 has to go through network address translation, which adds latency to the connection. The difference may be barely noticeable or extremely aggravating. When large scale NAT is in use (this is sometimes given the ridiculous name "carrier grade NAT") as it is on almost all mobile networks and many cable/*DSL ISPs, your IPv4 connections may also be unreliable. IPv6 connections do not need to pass through any sort of NAT, and do not suffer from the latency and reliability problems associated with NAT and large scale NAT. This issue will also affect Android apps which connect to IPv6 enabled web sites.
The sites (and apps) where you may have problems are small and large, starting with Google, Facebook, Wikipedia...
There is a very tiny (but growing) number of sites which use only IPv6, because there aren't any IPv4 addresses left for them to use. You won't be able to access these sites at all. You will only receive an error message.