Connected speech is a skill that is learned once you can pronounce words accurately.
It decreases the accuracy of some sounds you make (is he becomes izzee), and moves some final sounds from one word to the next (his pan becomes hizpan). Connected speech is not a goal in itself; for native speakers, it is the byproduct of English rhythm and idea grouping.
English rhythm sets a pace for speaking, with stressed words “on” the beat, and less important words “between” the beats. To keep this pace, less important words are shortened, sounds are relaxed, and words are connected.
This ensures that the beats carry the most important words—which are spoken accurately and clearly and with more stress—making them stand out acoustically from the other words spoken, which have been reduced and are less clear, less stressed, and often run together/connected.
(This is much easier to demonstrate than explain)
I don’t want you to think that the beats always fall exactly at equally-measured points in time—they don’t—because important words and phrases will have differing numbers of modifiers, descriptors and grammatical markers following them. Imagine a skyline where you see hill after hill after hill, from left to right, across your view. Your important words are on the hills of your sound, and everything else is in the valleys between the hills. Connected speech happens mostly in the valleys.
If a person that can pronounce every word accurately, the next step is to learn how to connect ideas ( stress & intonation) and words (connected speech) to become a more coherent and fluid speaker of English.
It’s extremely difficult for native speakers to understand someone who speaks word by word with breaks in between, even if they are accurately pronounced. It’s the groupings of words that convey your ideas—the hills and valleys.