Miners are essentially trying to guess numbers that fit some criteria.
ᴡʜᴇʀᴇ ᴛʜᴇ ᴘᴜᴢᴢʟᴇ ᴍᴀᴛʜ ᴘʀᴏʙʟᴇᴍꜱ ᴀʀᴇ ᴄʀᴇᴀᴛᴇᴅ
A puzzle assumes there is one solution. There are actually endless "solutions" for each new block, they're just very hard to find. In fact, there is no known way to find them other than trial-and-error.
The network hashrate shows you how many hashes (guesses) were done per second in order to "find" a correct answer for the most recent block.
For example now the hashrate is 200 exahashes per second = 200 x 10^18 guesses every second.
ᴡʜᴇʀᴇ ɪꜱ ᴇᴀᴄʜ ʙʟᴏᴄᴋ'ꜱ ᴄᴏʀʀᴇᴄᴛ ᴀɴꜱᴡᴇʀ ɢᴇɴᴇʀᴀᴛᴇᴅ ᴛᴏ ʙᴇ ꜱᴏʟᴠᴇᴅ?
  1. There is no one correct answer, there are many.
  2. The correct answers are not known in advance, they are "discovered" through mining. What is known in advance is the criteria by which to judge if an answer is correct or not. That criteria changes with every block and even with every attempted guess (via the so-called nonce explained in the comment from @nullcount).