Rhizoids are thread-like growths from the base or bottom of a plant, found mainly in lower groups such as algae, fungi, bryophytes and pteridophytes, that function like roots of higher plants (Gymnosperm and angiosperm).
Origin of plant occurred in water from where it gradually migrated to land during long course of evolution. In water or near it, plant could absorb water (to carry out its physiological processes) from all its sides easily and there was no need of any special absorbing organ ( i.e. roots). Additionally, in primitive state, tissue differentiation and division of labor was minimum in plants, thus not requiring water in differential amount for their various parts and tissues. Once, the plant came to land, it immediately required well developed root system to absorb water efficiently, and also to get anchored to the land.
The rhizoids are just threads and function in that way. They do not absorb water as the root does by a developed mechanism. Rhizoids absorb water by capillary action as the wick made of thin threads in an old oil lamp absorbs oil. Water moves up between threads of rhizoids and not through each of them as in roots.

In fungi, rhizoids are small branching hyphae that grow downwards from the stolon

Stolon

In biology, stolons are horizontal connections between organisms. They may be part of the organism, or of its skeleton; typically, animal stolons are external skeletons.-In botany:...

s that anchor the fungus. They release digestive enzyme

Enzyme

Enzymes are proteins that catalyze chemical reactions. In enzymatic reactions, the molecules at the beginning of the process, called substrates, are converted into different molecules, called products. Almost all chemical reactions in a biological cell need enzymes in order to occur at rates...

s and absorb digested organic material.
In land plants, rhizoids are trichome

Trichome

Trichomes are fine outgrowths or appendages on plants and certain protists. These are of diverse structure and function. Examples are hairs, glandular hairs, scales, and papillae.- Algal trichomes :...

s that anchor the plant

Plant

Plants are living organisms belonging to the kingdom Plantae. Precise definitions of the kingdom vary, but as the term is used here, plants include familiar organisms such as trees, flowers, herbs, bushes, grasses, vines, ferns, mosses, and green algae. The group is also called green plants or...

 to the ground. In the liverworts

Marchantiophyta

The Marchantiophyta are a division of bryophyte plants commonly referred to as hepatics or liverworts. Like other bryophytes, they have a gametophyte-dominant life cycle, in which cells of the plant carry only a single set of genetic information....

, they are absent or unicellular, but multicelled in moss

Moss

Mosses are small, soft plants that are typically 1–10 cm tall, though some species are much larger. They commonly grow close together in clumps or mats in damp or shady locations. They do not have flowers or seeds, and their simple leaves cover the thin wiry stems...

es. In vascular plant

Vascular plant

Vascular plants are those plants that have lignified tissues for conducting water, minerals, and photosynthetic products through the plant. Vascular plants include the clubmosses, Equisetum, ferns, gymnosperms and angiosperms...

s they are often called root hairs, and may be unicellular or multicellular.

In certain algae

Algae

Algae are a large and diverse group of simple, typically autotrophic organisms, ranging from unicellular to multicellular forms, such as the giant kelps that grow to 65 meters in length. They are photosynthetic like plants, and "simple" because their tissues are not organized into the many...

, there is an extensive rhizoidal system that allows the alga to anchor itself to a sandy substrate

Substrate (biology)

In biology a substrate is the surface a plant or animal lives upon and grows on. A substrate can include biotic or abiotic materials and animals. For example, encrusting algae that lives on a rock can be substrate for another animal that lives on top of the algae. See also substrate .-External...

from which it can absorb nutrients.