Repo rate is the rate at which RBI lends money to all the banks. So if RBI hikes its repo rate, it becomes costly for banks to borrow money from RBI so they in turn hike the rates at which customers borrow money from them to compensate for the hike in repo rate.
Banks offer loans like home loans and auto loans to someone at an interest rate which is directly proportional to Repo rate. Now with the increase of 0.25% in repo rate, this increase will directly be passed to a common man.
Interest rate for common man will be repo rate plus the rate of interest on which he took the loan from the bank. So, if repo rate increases the interest rate of the loan will also increase. Thus increasing the EMI.
For example: If you had bought a house worth 30 lacs @10% interest, 15 yrs tenure, then the EMI would be Rs 32,238. With an increase of 0.25% in interest, your EMI will rise to Rs 32698.53.
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