Why is my child tax credit so much higher this year? ($4974 this year, $250 last year)

The child tax credit is higher for 2021 returns.   It is a refundable credit of $3600 per child under the age of 6 and $3000 per child 6 or older up to age 17.

Your CTC will be shown on line 28 of your Form 1040.

PREVIEW 1040

https://ttlc.intuit.com/questions/1901539-how-do-i-preview-my-turbotax-online-return-before-filing

Click on Tax Tools on the left side of the screen. Click on Tools. Click on View Tax Summary. Click on Preview my 1040 on the left side of the screen.

https://ttlc.intuit.com/questions/1900923-what-is-the-child-tax-credit

And did you get any of the Advance Credit during the year?  They may have sent you like half of the credit as an advance.  You would get IRS letter 6419 saying how much they sent you.  Be sure to enter it in your return so it doesn't try to give it to you again on line 28.  

For 2021, the child tax credit was expanded both in scope and amount. 

For 2020, the credit was $2000 per child under 17. For 2021, the child tax credit is $3,600 for each child under age 6 by the end of 2021 and $3,000 for each child between 6 and 18.

In your case the credit phaseout must have played a role. If your income is more than $200,000 ($400,000 for married filing jointly) the allowed amount is reduced. 

At this time, the bill to extended this credit beyond 2021, has not passed the Senate. If it does not pass, the credit will return to its 2020 levels for 2022.