Composing is improvising without a time constraint.
When we reference context we are talking about harmonic information that has occurred within a specific time frame in the past.
Let's say you've come up with a chord progression and it's context has mainly been the ais: 0 4 6 7 9 10, then you can use that information to your advantage, for example let's say you want to continue that same feeling, well then you can continue to use chords which use those ais and continue like that.
Alternatively you could have another set of ai's you want to switch to, say 0 3 6 7 8 10 then you could start introducing these new notes over time to have a sort of fade-in effect or you could go with an abrupt change which will have a different effect on the listener.
As long as you are aware of the harmonic context then you will be able to come up with harmony and melody which are dynamic.
Note: The reason why we talk about context in the composing section is that most of the time improvisation is done over a set of static changes which vary a little bit, but you are not in control of them, when you're composing you get to choose the changes. Although when you are playing solo then you can decide the changes and improvise too.
When you compose something it lets you be mostly free of your instrument and so you are not biased or restrained by your instrument.
This is beneficial in many ways, one way that it's beneficial is that it helps get rid of any bias that you have built up by using your instrument. Additionally, when you create ideas without your instrument then you'll create ideas which you might have thought impossible to play on the instrument, so when you try and play it becomes a workout, and you'll force yourself out of your comfort zone.
If you're goal is improvising then composing is also very useful as you can think about it as "slowed down" improvising. That means that anything you were able to think of while composing is technically possible when you're improvising, but you'd have to get it up to speed.
Additionally when you're improvising you're usually time restricted and sometimes if you get into a situation where you are unsure of what to do you will "escape" by doing something easy. When you're composing you don't have this problem and so you'll be able to come up with ideas which will help you in situations when you're improvising.
Just like anything else when you slow a process down and analyze what is occurring you are able to realize mistakes and things you'd like to improve.