The word 'strong' means the opposite of weak. So for example "A strong person can lift a heavy weight, or cope with a difficult situation." - the first being physical strength and the second being emotional.
However, 'strong' is often used in phrases that signify a big number. In this case 'a million'.
So 'A Million Strong' means both a big number and an organisation which is resilient, partly because of the big number of people.