You must pay for a seat if travelling with under-12s
If you're travelling with children under 12, at least one adult in the party must pay extra to reserve a seat - once you've done so, you get free allocated seating for the children (max four children per adult).
You'll pay a reduced £4 fee to do so, and can opt to sit in rows 18 to 30 with your children. If you choose to sit anywhere else, you'll need to pay full price for you and the children.
For children 12 and over, this isn't mandatory. You can chance it and not pay, in which case you'll be randomly allocated seats at check-in. Alternatively, you can pay to reserve seats for both adults and children - prices vary from £8 to £15 per seat, per flight (£9 to £22.50 at the airport), though Ryanair does sometimes have offers on allocated seating costs.
If you choose not to pay for seats and end up seated away from your kids, contact Ryanair customer services - they may be able to help.