I am trying to blast my sequence against primate databases remotely. But there are so many databases, and most are in abbreviation. Can you explain what they are in the below example list?

chimp AACZ contigs
chimp AADA contigs
chimp bes
chimp est
chimp htgs
chimp all contig
chimp refseq contig

and which one should I use for NGS reads?

It will be good, if you can give more details about what kind of reads you have and what are you going to do with them using blast. If you are going to align reads using blast, then Pierre's suggestion is right. For the databases (as far as I know)-

chimp AACZ contigs

chimp AADA contigs

AACZ and AADA are prefix of accession numbers. Both of them contains sequences from whole genome shotgun and have different entries. Look at this and you can find information for both of them.

chimp bes

This are the entries from BAC end sequences and you can read little bit about the genome here and here(this one is not for chimp but give you little idea about bac)

chimp est and chimp htgs stands for express sequence tags and high throughput genome sequences

chimp all contig will include all the contigs (different assembled versions and entries) and chimp refseq contig will align against reference sequences only.