only ~ 34% of the last blocks have signalized segwit support (https://coin.dance/blocks)
That would mean hardforking, and that would be not good
On August 1st, there will be a Bitcoin Improvement Proposal called BIP 148. This is a User Activated Soft Fork (UASF).
If 50% hashrate doesn't signal BIP 148 support by that point (it won't), there will be a chain split and you will have an equal number of coins on each chain - the BIP 148 chain will have SegWit. For a while it'll be a complete clusterfuck to find a dominant chain unless BIP 148 has obviously failed, and in my view it won't actually work and the legacy chain will stay as the majority chain.
The point of the split is for the economic majority to decide whether SegWit is worth it, because in the long run miners have to act based on their economic interests or they run out of money.
BITMAIN has given opposition to this in the form of a "User Activated Hard Fork", which I regard to be pretty evil. You can read about it on their blog post. If this chain is created, they will almost certainly be capable of 51% attacks on it for a long time.
Do I have to download another blockchain, or what does that mean for me?
At the moment I am using Bitcoin Core 14.1