partialTicks is used to smooth animation by interpolating between ticks. For example (code from PneumaticCraft: Repressurized to smoothly animate rotations of the Assembly Drill - see https://github.com/TeamPneumatic/pnc-repressurized/blob/master/src/main/java/me/desht/pneumaticcraft/client/render/tileentity/RenderAssemblyDrill.java):
void renderModel(TileEntityAssemblyDrill te, float partialTicks) {
if (te != null) {
float[] renderAngles = new float[5];
for (int i = 0; i < 4; i++) {
renderAngles[i] = te.oldAngles[i] + (te.angles[i] - te.oldAngles[i]) * partialTicks;
}
renderAngles[4] = te.oldDrillRotation + (te.drillRotation - te.oldDrillRotation) * partialTicks;
model.renderModel(0.0625f, renderAngles);
} else {
model.renderModel(0.0625f, new float[]{0, 0, 35, 55, 0});
}
}
The rotation angles and previous rotation angles are stored in the TE - every tick, the angles are updated as appropriate and the previous angles are copied into te.oldAngles[] (multiple angles in this case, since it's a robot arm which has several points of rotation).
The actual render angles are calculated as an interpolation of the current and previous angles, based on partialTicks: renderAngle = oldAngle + (newAngle - oldAngle) * partialTicks.
Of course, this can also apply to any other rendering: translations, scaling etc. But that's the principle.