The arrows on Form 1040 signify two things:
They are used to highlight important, named summary lines that you may need to find later. For example, on the 2020 Form 1040, you'll find it for things like "Total income" (Line 9), "Adjusted gross income" (Line 11), "Total tax" (Line 24), "Total payments" (Line 33), "Refunded to you" (Line 35a), and "Amount you owe now" (Line 37).
The arrow is also used to highlight checkboxes and other non-dollar amount fields that they don't want you to miss. On this year's form, it is used, for example, on the "Schedule D not required" checkbox, all of the refund Direct Deposit fields, and the Third Party Designee selection checkboxes.
These arrows have been on the 1040 form for a very long time. Take a look at the 1950 version of 1040:
Here you can see how the arrow was signifying that you should total the numbers above, but enter that total to the right. That is where the arrow came from.
Also on the 1950 form you can see it used to highlight an important non-monetary field:
In summary, the arrows highlight the most important fields, either so you don't accidentally skip them or to make it easier for you to find them when you review your finished form.