I don’t understand the meaning and usage of mal in this sentence:
Zuerst will ich mal mein Deutsch verbessern.
What of a difference would it make if there would be no mal?
I don’t understand the meaning and usage of mal in this sentence:
Zuerst will ich mal mein Deutsch verbessern.
What of a difference would it make if there would be no mal?
In this sentence the word »mal« is a modal particle.
In German there is a part of speach that doesn't exist in English: Modal particles. I have written about those words as an answer to another question: Modal particles
The best way to translate those words into any other language is to ignore them.
A modal particle for itself has no own meaning. It just influences the emotion that is transported with the sentence.
Those words emphasize the meaning of a sentence. One very important thing to know about modal particles ist, that 100 % of them have homonymes that are not modal particles. This makes it very hard for non-native-speakers to understand them, because when you look for the meaning of »mal«, »doch«, »aber«, »ja« and so on, you will always find the meaning of the non-modal twin.
I'm not super happy with the above answers. I agree that those small interjected words usually don't have a meaning in themselves and you could leave them out, but the tone of the sentence changes (see @chirlu comment to the @HubertSchölnast answer), especially in your example:
All in all, it always depends on the situation and they never have the exact same meaning. It is probably also very hard to learn those words from reading because they are used way more often in spoken language [citation needed ;-)].
It may mean nothing in particular at all but it may also imply that there are second thoughts, often with a bit of a tongue-in-cheek meaning as well:
Zunächst will ich einmal mein Deutsch verbessern.
Oh wait a moment, did I accidentially say "einmal" instead of "mal"? That's right because this is what the somewhat sloppy, colloquial "mal" stands for.
Now, if there is a "first", there probably (implied) is a "second", too:
Zunächst will ich einmal mein Deutsch verbessern.
Dann mache ich mir Sorgen darum, wie ich die Welt regiere.