A time series is a series of time points gathered in a vector. Example in Matlab:
t = 0:0.001:100 %this means from time t_start = 0 to t_end =100 seconds with 1 millisecond steps.
A Time table in Matlab is a table with the first column as the time series (usually in a date format of dd-mm-yy ) and some other columns defined by the user, for example, temperature, color, ph-value, etc.
For the converting part of your question, you want to use the time series as the first column of your time table, and then add other columns to it, so it isn't really a question of converting.