The following exerpt is taken from a journal article on the ways that parents influence the body image of their kids.  It is broken down and translated for your enhanced understanding.  

In addition to biological and psychological factors, modifiable social factors that include parent influences have been a major focus of theoretical and empirical investigations into the development of body image [10].

Translation:  There are factors that contribute to poor body image that are biological and psychological – such as genetic predisposition to eating disorders, a body type that doesn't conform to society's thin ideal, perfectionism, high emotional sensitivity, etc.  Society isn't to blame for negative body image in children (nor are parents); however, there are social/societal factors that DO contribute to a kid developing poor body image.  

In young children, it has been proposed that parents and family play a formative role in shaping the development of body size attitudes and body image, as the family may act as a filter that regulates the child’s exposure to media and prevailing cultural ideals [11].

Translation: Family does help shape a child's view on body sizes and shapes.  Kids learn a great deal about the world through the lens of a parent's eyes.  Parents determine, especially in young children, the types of messages kids are exposed to on TV, online, etc.  

Parents have been proposed to influence their children in numerous ways: their expressed evaluations about their own and each other’s bodies may serve as models for children to critique themselves and others [12,13];

Translation: The way that parents feel about and treat their own bodies influences how kids feel about their own bodies.  Calling yourself or another person fat or commenting on how good someone looks because they have lost weight sends the underlying message to your child that thin = good and fat = bad.  Your child will learn to evaluate their own body by the same standards.

their engagement in behaviours, such as exercising and dieting activities, may model the importance of adhering to cultural body size ideals [8,14];

Translation: "Do as I say, not as I do" is a saying that points out the discrepancy between our words and actions.  If you tell your kids stealing is wrong but then proceed to shoplift, they will internalize the message that stealing is ok.  Same with dieting.  If they see you doing it they will subconsciously develop the belief that dieting is a normal behavior.  Seeing a parent diet also sends the message that society's ideals around body image are accurate and desirable.  Your behavior probably matters even more than your words.  Kids are perceptive.  

and their direct instruction, comments, appearance criticism, and teasing may reinforce cultural body ideals and body size stigma [8,15].

Translation: Even worse than dieting or body bashing yourself is if you were to teach your kid how to diet and encourage it.  This implies that 1) there is something wrong and undesirable about their body, 2) that dieting can and will fix this, 3) that society's beauty standards should be accepted and abided to, and 4) that your love is conditional upon their appearance.  Is this really the message you want to send your child?  

There you have it, a breakdown of what a piece of research is saying about the influence of parents on their kids' body image.  For the full article and corresponding references, click here.