Each small element of a current-carrying conductor contributes a magnetic field proportional to the current, to the length of the element, and to the sine of the angle between the element and the line joining it to the point — and inversely proportional to the square of the distance from the element.
One element I·dl produces dB at P, perpendicular to both dl and r (here, into the page).
dB = (μ₀/4π) × I (dl × r̂) / r²
dB
field contribution of one element (teslas)
I dl
current element — current times a tiny length of wire
r
distance from the element to the point (metres)
In plain English: The magnetic cousin of Coulomb's law: add up the tiny field from every scrap of wire to get the total. Ampère's law is the shortcut when the geometry is symmetric; this works everywhere.
Where you'll meet it: Calculating the field of loops and coils where Ampère's law has no easy symmetry — e.g. the field at the centre of a single circular loop, a standard exam and viva question.