1. The underlying meaning:
What were people suffering from? The current wording suggests that both the mental illness and the families were the cause of suffering. Add some clarification after “and” (e.g., “and help their families, too”).
2. Verb tense:
Instead of the past progressive tense, which indicates that something continued to happen over time, use the simple past tense, indicating that it happened at a point in time. Change “wasn’t understanding” to “didn’t understand”.
3. Tense consistency:
Since the first verb uses in the simple past tense, the others should as well unless there is a good reason not to. Instead of “means” (simple present tense) use “meant” (simple past tense); instead of “has given” (present perfect) use “gave” (simple past); and instead of “was saying” (past progressive) use “said” (simple past).
For future possibility use “would”, not “will.”
“Them” is the 3rd person plural, direct object pronoun. In this case, use “those” to refer to people already mentioned or understood.
Use the plural form “families”, not the possessive “family’s”.
Remember to set off a non-essential (not grammatically needed) clause such as “in a speech he has given”, and remember to use a period after the abbreviation "Mr."
I didn’t understand what he meant when, in a speech he gave, Mr. Harper said the funding would help those suffering from mental illness and help their families, too.