In crypto-terms mining means adding a new block to the blockchain containing transactions.
Inorder to add a block to blockchain and get reward a miner should successfully hash the block.Successfully hashing a block means miner has to generate a hashcode containing certain number of leading zeroes. Number of zeroes is set by the difficulty level. So now what is Hashing. Hashing means taking a set of data and converting to a smaller value. For example if you give 'Tom' to a hash function it will give something like this "000856a73f0" Bit coin uses a hash function called double SHA-256. SHA means Secure Hash Algorithm. So every data you will get a hash of size 256 bits. Now lets look at a block to be added to a block chain.
A block contains following
Previous block hash,
Merkle root,
Timestamp
Nonce
Transactions
In this nonce is a random number. So what a mining system basically does is keep changing the nonce till it get hash with required number of zeroes. Once it get required zeroes the block is send to the network to get added to the previous block(block with previous hash) and the network agrees on that and the miner is rewarded.
My most upvoted post:
https://steemit.com/cryptourrency/@lmx3881/lmx-double-spending-problem-explained