Caveat; not a native speaker. Hopefully one will come along and clarify or correct anything I get wrong.
The regular imperfective of to write is писать. The usual perfective is написать. However, you can use different prefixes to express different nuances. In this case, записать. But what if you want to use that meaning as an imperfective? писать won't work, and записать has to be perfective. So then a new imperfective needs to be formed from the new perfective verb, and that's what записывать is.
If it was perfective future it would be запишете.
flootzavut is correct. That was a good piece of advice.
Nuance or a slightly different meaning is what prefixes are often used for. For example, "записать" means to record or to write down. You write all kind of stuff for different reasons, but when you record (when you note it down), you do it to "store" the information—be it someone's words, a note to buy eggs and milk or audio of an actor's voice).
Now, since "to record" might be an action performed repeatedly or as a prolonged process, you would ideally want an imperfective verb for it. How inconvenient would it be if we made up thousands of new shiny verbs but could not use them half of the time! Thankfully, Russian often forms a secondary imperfective using some suffix. -Ива/-ыва is a very frequent and productive one (for example, E-conjugation verbs behaving like читать use it very easily).
This is confusing for me. I can't think of any real scenario where someone writes something if thwy don't want to record or store that information.
Is писать only valid if you are waiting at the bus stop, you are bored and you decide to write something silly on the marquee?
Or if you are bored in class and you write "I am bored in class" in a piece of paper for no reason?
What verb should I use if I am writing a letter to my lover? And if I am writing financial records for an archive?
Записывать. It is a regular -ать verb, like читать.
Actually, this is true of all secondary imperfectives formed with -ывать/-ивать (the derivation is basically писать "write", imp. → записать "record", perf. → записывать "record", imp.), which makes читать-like verbs the most common class.
When languages are spoken at normal speed they often sound different frrom the written form. In English, "Do you want to go?" often sounds more like "Dyawannago?" This is not a matter of ignorance, it is just how people talk. Part of learning a language is tuning your mind and ears so you can recognize a spoken word in context even if it sounds a bit (or a lot) different from its written form.