"What is a genomic imprint? How does genomic imprinting take place?"
Genomic imprinting is an epigenetic mechanism of inheritance which allows genes to be expressed differently depending on which parent they come from. This means it is modification of the genome, or changes what the genome produces, without changing the nucleotide (DNA) sequence. The result of imprinting in diploid organisms is that one of the two alleles is silenced. This page provides a good overview of imprinting.
Two major mechanisms are proposed called DNA methylation and histone modification though others may yet be discovered. DNA methylation silences a gene by adding methyl groups to nucleotides (it modifies the nucleotide but not the sequence) which affects how they are expressed, whilst the exact mechanism is unknown (at least I can't find one on scholar) it does appear to be a key factor in some cancer growths. Genes can also be silenced by histone modification, binding a gene to histones reduces its activity, ie it produces less product.
Genomic imprinting was first described in Mealy Bugs (or at least this is one of the first described) which silence half of their genome in males. Whilst females are fully diploid, the male is also diploid but one half of the genome is silenced, making them effectively haploid. This is done by turning one half of the genome heterochromatic.
"If I say that "this" allele is maternally imprinted does it mean that
the allele of the gene is passed only by the mother? If a pedigree is
given, how can we identify whether the trait is paternally imprinted
or maternally imprinted?"
Specific control of a gene, rather than entire chromosomes described above, is only known in plants and some mammals. In this case, when a gene is imprinted, the gene is silenced. An example is Igf2 in mice described in the below diagram which is maternal imprinting (ie the mothers allele is silenced). When the mother has a mutant allele and the father a normal allele and normal offspring is produced. When the male passes on the Igf2 mutant the offspring is mutant because the mother's normal copy was imprinted.
The Igf2 gene can be seen in the above diagram. This is the one of the
first evidences of genomic imprinting discovered. In the first part of
the diagram a mutant gene trying to make the mouse offspring dwarf is
passed from the mother. It can be seen that the mouse is not dwarf
because the allele for size in this mouse is an imprinted. The
maternal allele is not expressed, so the dwarf trait is not expressed
in the offspring, only the normal size trait from the father is. In
the second part of the diagram the father passes on the mutant gene
and therefore all the offspring will be dwarf because the size trait
is completely dependent on the paternal allele, which in this case is
dwarf. - Creating Variation
The page this diagram and quote comes from also has a good section on genomic imprinting.