A resistor inline limits current to the capacitor. The current is what 'fills up' the capacitor.
Thus a higher series resistance makes it take longer to charge to a given volt level.
The volt level on the capacitor opposes an incoming signal (concept of a low pass filter).
I have Youtube videos which portray capacitor action visually. Current through wires is portrayed. Dynamic charge level on a capacitor is portrayed.
www.youtube.com/watch?v=eIWEU4pObJw
Equivalent Series Resistance comes into play when capacitors are used to filter a power supply. A capacitor with low ESR has a short time constant, and it works well at filtering ripple V at 50-60 Hz.
A capacitor with high ESR becomes 'sluggish' in comparison. It has a longer time constant. It becomes ineffective as a high pass filter.
Link to my Youtube video demonstrating this visually, over a range of ESR values:
www.youtube.com/watch?v=vm8wf7y94rM