What is Occupational Therapy? 
Occupational Therapy is a health profession dedicated to helping people with sensory, motor, and behavior problems perform their daily occupations to the best of their abilities. When working with a child, occupational therapists use purposeful activities to assist the child in performing their normal "occupations" of childhood, which include play, school-work, learning, and self-care/activities of daily living.

Some of the areas occupational therapy can help with: 

Fine motor skills & Handwriting
Gross motor skills
Endurance & muscle tone
Oral motor skills
Motor planning
Sensory processing & integration
Visual motor skills
Visual perception
Self-care skills

What is Sensory Integration? 

Sensory Integration (SI) is the ability to take in information through the five basic senses plus the sensations of movement (vestibular) and body position (proprioceptive) and use this information to produce adaptive responses or behaviors. SI dysfunction is a complex neurological disorder, manifested by difficulty detecting, modulating, discriminating or integrating sensation adaptively. When the process is disordered, a number of problems in learning, development or behavior may be evident. Sensory integrative therapy involves creating a playful environment that facilitates activities to help the body learn, organize, and process sensory information more efficiently.

Below are some symptoms that may indicate a dysfunction in sensory integration: 

Easily distracted
Poor coordination
Poor handwriting
Picky eater
Poor safety awareness
Difficulty with transitions
Poor body awareness
Low muscle tone or endurance
Activity level that is unusually high or low
Overly sensitive to touch, sound, movement, sight
Emotionally "up and down"
Avoids playground activities or sports
Difficulty completing activities of daily living
Shuts down or has meltdowns
Difficulty following directions
Difficulty unwinding or calming self
Delay in speech, motor, or academic achievement

The list above is not all-inclusive. A child with SI problems may just have some of these symptoms and the degree to which they exhibit them may vary. The important thing in determining a problem is how much it interferes with the child's functioning at home and school and how it affects the child's self-esteem.