An angle that measures more than 0 degrees and less than 90 degrees is called an acute angle. Let's understand the different types of angles and why an acute angle fits the given criteria.

1. Right angle:
A right angle measures exactly 90 degrees. It forms a perfect "L" shape, with one straight line meeting another at a 90-degree angle.

2. Acute angle:
An acute angle measures less than 90 degrees. It is smaller than a right angle but bigger than a zero-degree angle. Acute angles are commonly seen in everyday objects and shapes, such as the corners of a triangle or the angles of a square.

3. Obtuse angle:
An obtuse angle measures more than 90 degrees but less than 180 degrees. It is larger than a right angle and appears wider in comparison to an acute angle.

4. Straight angle:
A straight angle measures exactly 180 degrees. It forms a straight line, where two straight lines meet and create a single straight path.

Given the options, the angle that falls between 0 and 90 degrees is an acute angle. Let's look at the other options to understand why they are not correct for this question:

a) Obtuse angle: An obtuse angle measures more than 90 degrees, which does not fit the given criteria of measuring less than 90 degrees.

c) Right angle: A right angle measures exactly 90 degrees, which is not less than 90 degrees as required by the question.

d) Straight angle: A straight angle measures exactly 180 degrees, which is more than 90 degrees and does not fit the given criteria.

Therefore, the correct answer is option 'B' - Acute angle, as it measures more than 0 degrees and less than 90 degrees.