I'm your mother, so I can pay for your flight for you.
My mom’s nose hair is long.
This word starts with お which makes it more polite. Then, there's the kanji 母 which you know means mother. Last, there's the honorific さん which further adds respect (to the mother). So, this is the nice way to say mother. You use it when you're talking to your own mom or talking about her with friends. You can also use this when you're talking about your friends' moms.
If you need to talk about someone's mother that you don't really know, or you aren't close to, you'll want to use お母様, instead. Don't worry, you'll learn that last kanji in a few lessons. Until then, it's pronounced, おかあさま. Kay?
Since this word is made up of a single kanji, it uses the kun'yomi reading. You have to remember the かあ portion. Here's a mnemonic to help you to remember it:
What does your super nice mother do for you (this is why you're so polite to her!)? She drives you all around in her car (かあ) taking you wherever you need to go... soccer, kendo, whatever. What a nice mother you have!