I am new to D&D and have recently bought the Starter Set for 5e (Lost Mines of Phandelver). So I was looking through the spells and I see some spells that can be used in battle can take minutes to cast and each round in battle is 6 seconds of in-game time. In this case I was looking at prayer of healing (since I'm being a Cleric) and it says prayer of healing takes 10 minutes to cast. So does this mean it will take 100 battle rounds to cast it?
Yes, prayer of healing would take 100 combat rounds to cast, if you tried to cast it during combat. Additionally, the cleric would also have to avoid being attacked to maintain Concentration: getting hit would initiate a Constitution Check against DC 10 or half of the damage taken, whichever is higher.
For this reason, spells that take more than an Action for their casting time aren't typically used during combat. Instead, use them during periods of narration, after combat, or in anticipation of combat. Your in-combat healing comes from faster spells like cure wounds and healing word.
Caveat: an additional in-combat healing method could be a variant human with the Healer feat, but the scope of the question is the Phandelver Starter Set.